On impact of statistical estimates on precision of stochastic optimization

This paper studies the consequences of imperfect information for the precision of stochastic optimization. In particular, it is assumed that the stochastic characteristics of an optimization problem depend on unknown parameters estimated from available data. First, a theoretical result is presented, showing that consistent parameters estimation leads to consistent optimization. Further, a type of the studied models is specified; it is assumed that the random variables present in the optimization problem are influenced by covariates. This influence is expressed via a parametric regression model, whose parameters have to be estimated and used instead of the unknown correct parameters values. The objective is then to explore, with the aid of simulations, the imprecision of the optimization based on these estimates. Several types of regression models are recalled, the variability of estimates and the related precision of sub-optimal solutions is studied in detail on an example dealing with optimal maintenance. The impact of random right-censoring on the deterioration of precision is studied as well.